The couple wed in 2004 and share two children together

In new court documents filed Feb. 23 and obtained by PEOPLE, Dane’s response mirrors Gayheart‘s petition for the dissolution of their marriage.

Like Gayheart, Dane filed for joint legal and physical custody of the pair’s two children: daughters Billie, 7, and Georgia, 6.

Dane, 45, also cited irreconcilable differences and requested to pay spousal support to Gayheart, 46.

Earlier this month, PEOPLE confirmed that the couple — who wed Aug. 29. 2004 — had decided to end their marriage of 14 years after Gayheart, best known for films such as Jawbreaker and Scream 2, had filed.

“After 14 years together we have decided that ending our marriage is the best decision for our family,” Dane, 45, said in a statement to PEOPLE. “We will continue our friendship and work as a team to co-parent our two beautiful girls as they are the most important thing in the world to us. We kindly ask that you respect our privacy during this time as we navigate the next phase of our lives.”

Credit: Matt Winkelmeyer/Getty Images

Gayheart and the former Grey’s Anatomy star — he rose to fame as Dr. Mark Sloan in the ABC drama have faced a number of challenges over the course of their relationship.

In 2009, an intimate video of Dane, Gayheart and another woman was released without their knowledge. Two years later, Dane entered into rehab for an addiction to painkillers following a sports injury.

Speaking to PEOPLE in 2014, the actor said, “We’ve all made mistakes. My one regret is that I got the person I love most wrapped up in all that: Rebecca.”

Of his family life, Dane said he feels happiest when he’s at home with them.

“I never had a family, and now I do,” he said, noting his father died when he was 7. “I know I’m a very lucky guy.”